To make broccoli cheddar soup in the Crock Pot, sauté 1 cup of onion in 1/4 cup of butter for approximately four minutes. Stir 1/4 cup of flour into the pan, whisking it to combine the flour completely. Slowly, stir 1 can of evaporated milk into the pan.
Cook the milk, whisking it constantly, until the mixture is smooth. Transfer it to the crock of a slow cooker. Add 1 thawed bag of frozen broccoli florets, 32 ounces of chicken broth, 1/4 teaspoon of salt and 1/2 teaspoon of black pepper. Cover the slow cooker, and cook the soup on low for four hours. Then, add 8 ounces of cubed cheese, 1 1/2 cups of shredded cheddar and 1 cup of shredded Parmesan. Stir the soup until the cheeses melt.
Alternatively, sauté 1 1/2 cups of chopped onion in 1/3 cup butter. Cook the onions for three minutes before adding 2 cloves of minced garlic and 6 tablespoons of flour, Stir the mixture constantly, and cook it for two minutes before adding two 12-ounce cans of evaporated milk. Cook the mixture until it starts thickening, and transfer it to the slow cooker. Add 5 cups of chicken broth, 4 cups of fresh broccoli florets and 1/8 teaspoon dried thyme. Cover and cook the soup on high for three hours or on low for six hours. Reduce the slow cooker's heat to warm before adding 1/2 cup of heavy cream, 12 ounces of sharp cheddar cheese and 2 ounces of Parmesan.